For the specific case of binary stars, this paper presents signal-to-noise ratio (SNR) calculations for the detection of the parity (the side of the brighter component) of the binary using the double correlation method. This double correlation method is a focal plane version of the well-known Knox-Thompson method used in speckle interferometry. It is shown that SNR for parity detection using double correlation depends linearly on binary separation. This new result was entirely missed by previous analytical calculations dealing with a point source. It is concluded that, for magnitudes relevant to the present day speckle interferometry and for binary separations close to the diffraction limit, speckle masking has better SNR for parity detection.